One Hundred Twenty-Seven Subsemilattices and Planarity
Gábor Czédli · Order · 2019
Abstract Let L be a finite n-element semilattice. We prove that if L has at least 127 ⋅ 2n− 8 subsemilattices, then L is planar. For n > 8, this result is sharp since there is a non-planar semilattice with exactly 127 ⋅ 2n− 8 − 1 subsemilattices.